**Time limit:**1.00 s**Memory limit:**512 MB

Syrjälä's network has n computers and m connections between them. The network consists of components of computers that can send messages to each other.

Nobody in Syrjälä understands how the network works. For this reason, if a connection breaks down, nobody will repair it. In this situation a component may be divided into two components.

Your task is to calculate the number of components after each connection breakdown.

# Input

The first input line has three integers n, m and k: the number of computers, connections and breakdowns. The computers are numbered 1,2,\dots,n.

Then, there are m lines describing the connections. Each line has two integers a and b: there is a connection between computers a and b. Each connection is between two different computers, and there is at most one connection between two computers.

Finally, there are k lines describing the breakdowns. Each line has two integers a and b: the connection between computers a and b breaks down.

# Output

After each breakdown, print the number of components.

# Constraints

- 1 \le n \le 10^5
- 1 \le m \le 2 \cdot 10^5
- 1 \le k \le m
- 1 \le a,b \le n

# Example

Input:

5 5 3 1 2 1 3 2 3 3 4 4 5 3 4 2 3 4 5

Output:

2 2 3